The miniaturization of loudspeakers has been a trend since the early days of domestic high-fidelity music systems. Space constraints and aesthetics are the driving forces for speaker miniaturization, and have been assisted by developments in transducer design and digital electronics. Presently, loudspeaker systems can be miniaturized to the point where the limiting factor is the physical realization of the enclosure, including the enclosure's size.
In the art of loudspeaker systems it is desirable to obtain an extended low frequency response. In addition, it is generally desirable to minimize the size of the loudspeaker enclosure, for example to reduce cost and allow for more flexible placement. These two goals are often in opposition, and it is well known that obtaining extended low frequency response typically requires large, floor standing speakers with significant internal volumes, and/or large diameter woofers. Both options require tradeoffs in terms of efficiency, cost and flexibility of use, with large speakers typically being less efficient, costing more, and being less flexible in terms of placement in a listener's home.
Among low frequency loudspeaker systems, the class known as “reflex systems” has approximately a 6 decibel (dB) advantage in efficiency/bandwidth over a simple sealed box loudspeaker. Accordingly, these reflex systems are commonly the system of choice where an extended low frequency response in a small device is desired. A reflex system loudspeaker can be implemented by constructing a duct, for example, a tube, connecting the interior of the loudspeaker enclosure to the outside environment. In operation of the loudspeaker, the air inside the duct becomes an acoustic mass, and the air within the enclosure is an acoustic compliance or spring. The acoustic mass and spring together create a second order filter system, which when combined with the natural second order response of the loudspeaker transducer, creates a fourth order high pass filter. This fourth order filter may exhibit approximately a 24 dB/octave attenuation of the low frequencies, for example. This system becomes increasingly difficult to realize with high performance miniature low frequency transducers because the necessary duct dimensions and volume approach or surpass those of the enclosure itself. Additionally, long duct tubes produce distortions of the acoustic output, for example, pipe resonances and other noise, which may render the system unusable, particularly in high performance applications.
An alternative implementation of a reflex system replaces the duct with a passive radiator. A passive radiator is essentially a loudspeaker without a magnet or voice coil. A passive radiator system may replicate the intended response of a vented system without the physical size and volume of the duct, producing a further miniaturized loudspeaker system. This may be accomplished by attaching a substantial weight to the passive radiator, which resonates with the compliance of the enclosed air in the loudspeaker enclosure. This weight can be approximately 10-50 times that of the moving mass of the active transducer. Modern loudspeaker systems may be constructed using lightweight, rigid space frames and miniature Neodymium magnet structures in low frequency transducers. In such systems, the passive radiator mass in vibratory motion can physically knock the loudspeaker onto its side, or cause it to move across surfaces and potentially fall. Accordingly, the stability, and hence the usefulness, of such systems is limited. In order to tune the passive radiator(s) in a small enclosure to a very low frequency, a great deal of mass must be added to the passive radiator(s), and the more mass added, the lower the resonant frequency of the radiator. There is also another dimension to the passive radiator(s) known as the compliance. Typically, the suspension of the radiator/driver acts as a mechanical spring that has damping properties and contributes to losses in the system. Increasing the mass of the radiators can negatively impact low frequency performance, particularly if the radiators are downward facing, since the high mass causes the suspension of the passive radiators to sag.
Assume for example, a rectilinear loudspeaker enclosure housing a woofer, on any of the six surfaces, and a single passive radiator on one vertical face. The stability of the system will be affected by the movement and location of the passive radiator, and the weight distribution of the system as a whole. There are two break points in system stability. First, when the force generated by the movement of the passive radiator shifts the center of gravity of the system such that the measured weight on one extreme side of the base of the loudspeaker system is countered or exceeded by this force, the enclosure will begin to rock back and forth. Second, if the force created by the mass times the acceleration of the passive radiator's movement exceeds the measured mass of the loudspeaker system at one extreme of the base of the loudspeaker system, and continues for a period of time of sufficient duration to move the center of gravity outside of the base of the loudspeaker system, the vertical integrity of the loudspeaker system will be compromised, and the loudspeaker may fall over. For example, the force created by 200 Hz raised cosine waveform is approximately ten times greater than at 20 Hz, and while lasting only one-tenth as long can be sufficient to easily destabilize a loudspeaker system. These stability concerns are scalable, and apply to any size loudspeaker system.